There are enough Azumaya algebras on surfaces
classification
🧮 math.AG
math.AC
keywords
surfacesalgebraicbrauergroupnormalalgebrasapplicationazumaya
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Using Maruyama's theory of elementary transformations, I show that the Brauer group surjects onto the cohomological Brauer group for separated geometrically normal algebraic surfaces. As an application, I infer the existence of nonfree vector bundles on proper normal algebraic surfaces.
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